415:, which occurs within the brain on the order of milliseconds. The brain must obtain a large quantity of information based on a relatively short neural response. Additionally, if low firing rates on the order of ten spikes per second must be distinguished from arbitrarily close rate coding for different stimuli, then a neuron trying to discriminate these two stimuli may need to wait for a second or more to accumulate enough information. This is not consistent with numerous organisms which are able to discriminate between stimuli in the time frame of milliseconds, suggesting that a rate code is not the only model at work.
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information, a more consistent, regular firing rate would have been evolutionarily advantageous, and neurons would have utilized this code over other less robust options. Temporal coding supplies an alternate explanation for the “noise," suggesting that it actually encodes information and affects neural processing. To model this idea, binary symbols can be used to mark the spikes: 1 for a spike, 0 for no spike. Temporal coding allows the sequence 000111000111 to mean something different from 001100110011, even though the mean firing rate is the same for both sequences, at 6 spikes/10 ms.
688:) attempt to automatically find a small number of representative patterns which, when combined in the right proportions, reproduce the original input patterns. The sparse coding for the input then consists of those representative patterns. For example, the very large set of English sentences can be encoded by a small number of symbols (i.e. letters, numbers, punctuation, and spaces) combined in a particular order for a particular sentence, and so a sparse coding for English would be those symbols.
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directions. However it fires the fastest for one direction and more slowly depending on how close the target was to the neuron's "preferred" direction. If each neuron represents movement in its preferred direction, and the vector sum of all neurons is calculated (each neuron has a firing rate and a preferred direction), the sum points in the direction of motion. In this manner, the population of neurons codes the signal for the motion. This particular population code is referred to as
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nerve. The first ALSR representation was for steady-state vowels; ALSR representations of pitch and formant frequencies in complex, non-steady state stimuli were later demonstrated for voiced-pitch, and formant representations in consonant-vowel syllables. The advantage of such representations is that global features such as pitch or formant transition profiles can be represented as global features across the entire nerve simultaneously via both rate and place coding.
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given odorants. This type of extra information could help in recognizing a certain odor, but is not completely necessary, as average spike count over the course of the animal's sniffing was also a good identifier. Along the same lines, experiments done with the olfactory system of rabbits showed distinct patterns which correlated with different subsets of odorants, and a similar result was obtained in experiments with the locust olfactory system.
994:. If the number of basis vectors n is equal to the dimensionality k of the input set, the coding is said to be critically complete. In this case, smooth changes in the input vector result in abrupt changes in the coefficients, and the coding is not able to gracefully handle small scalings, small translations, or noise in the inputs. If, however, the number of basis vectors is larger than the dimensionality of the input set, the coding is
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statistically or probabilistically. They may be characterized by firing rates, rather than as specific spike sequences. In most sensory systems, the firing rate increases, generally non-linearly, with increasing stimulus intensity. Under a rate coding assumption, any information possibly encoded in the temporal structure of the spike train is ignored. Consequently, rate coding is inefficient but highly robust with respect to the ISI '
636:
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In studies dealing with the front cortical portion of the brain in primates, precise patterns with short time scales only a few milliseconds in length were found across small populations of neurons which correlated with certain information processing behaviors. However, little information could be determined from the patterns; one possible theory is they represented the higher-order processing taking place in the brain.
98:. These differ from action potentials because information about the strength of a stimulus directly correlates with the strength of the neurons' output. The signal decays much faster for graded potentials, necessitating short inter-neuron distances and high neuronal density. The advantage of graded potentials is higher information rates capable of encoding more states (i.e. higher fidelity) than spiking neurons.
281:, at least, information is not simply encoded in firing but also in the timing and duration of non-firing, quiescent periods. There is also evidence from retinal cells, that information is encoded not only in the firing rate but also in spike timing. More generally, whenever a rapid response of an organism is required a firing rate defined as a spike-count over a few hundred milliseconds is simply too slow.
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similar responses in terms of spike count. The temporal component of the pattern elicited by each tastant may be used to determine its identity (e.g., the difference between two bitter tastants, such as quinine and denatonium). In this way, both rate coding and temporal coding may be used in the gustatory system – rate for basic tastant type, temporal for more specific differentiation.
117:) between two successive spikes in a spike train often vary, apparently randomly. The study of neural coding involves measuring and characterizing how stimulus attributes, such as light or sound intensity, or motor actions, such as the direction of an arm movement, are represented by neuron action potentials or spikes. In order to describe and analyze neuronal firing,
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226:. As the weight of the stimulus increased, the number of spikes recorded from sensory nerves innervating the muscle also increased. From these original experiments, Adrian and Zotterman concluded that action potentials were unitary events, and that the frequency of events, and not individual event magnitude, was the basis for most inter-neuronal communication.
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what neural coding strategy is being used. Temporal coding in the narrow sense refers to temporal precision in the response that does not arise solely from the dynamics of the stimulus, but that nevertheless relates to properties of the stimulus. The interplay between stimulus and encoding dynamics makes the identification of a temporal code difficult.
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theoretical point of view, population coding is one of a few mathematically well-formulated problems in neuroscience. It grasps the essential features of neural coding and yet is simple enough for theoretic analysis. Experimental studies have revealed that this coding paradigm is widely used in the sensory and motor areas of the brain.
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control spikes and therefore certain behaviors of the mouse (e.g., making the mouse turn left). Researchers, through optogenetics, have the tools to effect different temporal codes in a neuron while maintaining the same mean firing rate, and thereby can test whether or not temporal coding occurs in specific neural circuits.
298:(t;t+Δt) summed over all repetitions of the experiment divided by the number K of repetitions is a measure of the typical activity of the neuron between time t and t+Δt. A further division by the interval length Δt yields time-dependent firing rate r(t) of the neuron, which is equivalent to the spike density of PSTH (
294:(PSTH). The time t is measured with respect to the start of the stimulation sequence. The Δt must be large enough (typically in the range of one or a few milliseconds) so that there is a sufficient number of spikes within the interval to obtain a reliable estimate of the average. The number of occurrences of spikes n
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activity pattern across the population. The moving direction of the object is retrieved from the population activity, to be immune from the fluctuation existing in a single neuron's signal. When monkeys are trained to move a joystick towards a lit target, a single neuron will fire for multiple target
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As an experimental procedure, the time-dependent firing rate measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the coding scheme used by neurons in the brain. Neurons can not wait
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The spike-count rate, also referred to as temporal average, is obtained by counting the number of spikes that appear during a trial and dividing by the duration of trial. The length T of the time window is set by the experimenter and depends on the type of neuron recorded from and to the stimulus. In
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neurons, partly due to the relative ease of measuring rates experimentally. However, this approach neglects all the information possibly contained in the exact timing of the spikes. During recent years, more and more experimental evidence has suggested that a straightforward firing rate concept based
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With the development of large-scale neural recording and decoding technologies, researchers have begun to crack the neural code and have already provided the first glimpse into the real-time neural code as memory is formed and recalled in the hippocampus, a brain region known to be central for memory
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Sparse coding may be a general strategy of neural systems to augment memory capacity. To adapt to their environments, animals must learn which stimuli are associated with rewards or punishments and distinguish these reinforced stimuli from similar but irrelevant ones. Such tasks require implementing
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As a consequence, sparseness may be focused on temporal sparseness ("a relatively small number of time periods are active") or on the sparseness in an activated population of neurons. In this latter case, this may be defined in one time period as the number of activated neurons relative to the total
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present in the two spike trains about a stimulus feature. However, this was later demonstrated to be incorrect. Correlation structure can increase information content if noise and signal correlations are of opposite sign. Correlations can also carry information not present in the average firing rate
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To account for the fast encoding of visual stimuli, it has been suggested that neurons of the retina encode visual information in the latency time between stimulus onset and first action potential, also called latency to first spike or time-to-first-spike. This type of temporal coding has been shown
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Typically an encoding function has a peak value such that activity of the neuron is greatest if the perceptual value is close to the peak value, and becomes reduced accordingly for values less close to the peak value. It follows that the actual perceived value can be reconstructed from the overall
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of mice, first-spike latency relative to the start of a sniffing action seemed to encode much of the information about an odor. This strategy of using spike latency allows for rapid identification of and reaction to an odorant. In addition, some mitral/tufted cells have specific firing patterns for
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Research on mammalian gustatory system has shown that there is an abundance of information present in temporal patterns across populations of neurons, and this information is different from that which is determined by rate coding schemes. Groups of neurons may synchronize in response to a stimulus.
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For very brief stimuli, a neuron's maximum firing rate may not be fast enough to produce more than a single spike. Due to the density of information about the abbreviated stimulus contained in this single spike, it would seem that the timing of the spike itself would have to convey more information
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The temporal structure of a spike train or firing rate evoked by a stimulus is determined both by the dynamics of the stimulus and by the nature of the neural encoding process. Stimuli that change rapidly tend to generate precisely timed spikes (and rapidly changing firing rates in PSTHs) no matter
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Nevertheless, the experimental time-dependent firing rate measure can make sense, if there are large populations of independent neurons that receive the same stimulus. Instead of recording from a population of N neurons in a single run, it is experimentally easier to record from a single neuron and
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The spike-count rate can be determined from a single trial, but at the expense of losing all temporal resolution about variations in neural response during the course of the trial. Temporal averaging can work well in cases where the stimulus is constant or slowly varying and does not require a fast
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signals reflect population (network) oscillations. The phase-of-firing code is often categorized as a temporal code although the time label used for spikes (i.e. the network oscillation phase) is a low-resolution (coarse-grained) reference for time. As a result, often only four discrete values for
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to open, depolarizing the cell and producing a spike. When blue light is not sensed by the cell, the channel closes, and the neuron ceases to spike. The pattern of the spikes matches the pattern of the blue light stimuli. By inserting channelrhodopsin gene sequences into mouse DNA, researchers can
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patterns. However, functions of the brain are more temporally precise than the use of only rate encoding seems to allow. In other words, essential information could be lost due to the inability of the rate code to capture all the available information of the spike train. In addition, responses are
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A typical population code involves neurons with a
Gaussian tuning curve whose means vary linearly with the stimulus intensity, meaning that the neuron responds most strongly (in terms of spikes per second) to a stimulus near the mean. The actual intensity could be recovered as the stimulus level
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and the ability to represent a number of different stimulus attributes simultaneously. Population coding is also much faster than rate coding and can reflect changes in the stimulus conditions nearly instantaneously. Individual neurons in such a population typically have different but overlapping
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is useful for studying temporal coding because of its fairly distinct stimuli and the easily discernible responses of the organism. Temporally encoded information may help an organism discriminate between different tastants of the same category (sweet, bitter, sour, salty, umami) that elicit very
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The issue of temporal coding is distinct and independent from the issue of independent-spike coding. If each spike is independent of all the other spikes in the train, the temporal character of the neural code is determined by the behavior of time-dependent firing rate r(t). If r(t) varies slowly
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The link between stimulus and response can be studied from two opposite points of view. Neural encoding refers to the map from stimulus to response. The main focus is to understand how neurons respond to a wide variety of stimuli, and to construct models that attempt to predict responses to other
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The sparse code is when each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons. In contrast to sensor-sparse coding, sensor-dense coding implies that all information from possible sensor
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Population coding is a method to represent stimuli by using the joint activities of a number of neurons. In population coding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs. From the
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Place-time population codes, termed the averaged-localized-synchronized-response (ALSR) code, have been derived for neural representation of auditory acoustic stimuli. This exploits both the place or tuning within the auditory nerve, as well as the phase-locking within each nerve fiber auditory
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of macaques, the timing of the first spike relative to the start of the stimulus was found to provide more information than the interval between spikes. However, the interspike interval could be used to encode additional information, which is especially important when the spike rate reaches its
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are found to carry information, the neural code is often identified as a temporal code. A number of studies have found that the temporal resolution of the neural code is on a millisecond time scale, indicating that precise spike timing is a significant element in neural coding. Such codes, that
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anterior paired lateral (APL) neurons. Systematic activation and blockade of each leg of this feedback circuit shows that Kenyon cells activate APL neurons and APL neurons inhibit Kenyon cells. Disrupting the Kenyon cell–APL feedback loop decreases the sparseness of Kenyon cell odor responses,
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This type of code is used to encode continuous variables such as joint position, eye position, color, or sound frequency. Any individual neuron is too noisy to faithfully encode the variable using rate coding, but an entire population ensures greater fidelity and precision. For a population of
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Optogenetic technology also has the potential to enable the correction of spike abnormalities at the root of several neurological and psychological disorders. If neurons do encode information in individual spike timing patterns, key signals could be missed by attempting to crack the code while
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Rate coding is a traditional coding scheme, assuming that most, if not all, information about the stimulus is contained in the firing rate of the neuron. Because the sequence of action potentials generated by a given stimulus varies from trial to trial, neuronal responses are typically treated
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Neurons exhibit high-frequency fluctuations of firing-rates which could be noise or could carry information. Rate coding models suggest that these irregularities are noise, while temporal coding models suggest that they encode information. If the nervous system only used rate codes to convey
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A sequence, or 'train', of spikes may contain information based on different coding schemes. In some neurons the strength with which a postsynaptic partner responds may depend solely on the 'firing rate', the average number of spikes per unit time (a 'rate code'). At the other end, a complex
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has suggested that sparse coding increases the capacity of associative memory by reducing overlap between representations. Experimentally, sparse representations of sensory information have been observed in many systems, including vision, audition, touch, and olfaction. However, despite the
974:-like distribution, but peakier than Gaussian, with many zero values, some small absolute values, fewer larger absolute values, and very few very large absolute values. Thus, many of the basis vectors are active. Hard sparseness, on the other hand, indicates that there are many zero values,
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The time-dependent firing rate is defined as the average number of spikes (averaged over trials) appearing during a short interval between times t and t+Δt, divided by the duration of the interval. It works for stationary as well as for time-dependent stimuli. To experimentally measure the
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increases inter-odor correlations, and prevents flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor-specificity of memories.
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For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials. If Δt is small, there will never be more than one spike within the interval between t and t+Δt on any given trial. This means that r(t)Δt is also the
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In temporal coding, learning can be explained by activity-dependent synaptic delay modifications. The modifications can themselves depend not only on spike rates (rate coding) but also on spike timing patterns (temporal coding), i.e., can be a special case of
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of two pairs of neurons. A good example of this exists in the pentobarbital-anesthetized marmoset auditory cortex, in which a pure tone causes an increase in the number of correlated spikes, but not an increase in the mean firing rate, of pairs of neurons.
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unimodal tuning curves, i.e. with a single peak, the precision typically scales linearly with the number of neurons. Hence, for half the precision, half as many neurons are required. In contrast, when the tuning curves have multiple peaks, as in
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It has been shown that neurons in some cortical sensory areas encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network oscillatory fluctuations, rather than only in terms of their spike count. The
374:) are candidates for temporal codes. As there is no absolute time reference in the nervous system, the information is carried either in terms of the relative timing of spikes in a population of neurons (temporal patterns) or with respect to an
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small absolute values, fewer larger absolute values, and very few very large absolute values, and thus few of the basis vectors are active. This is appealing from a metabolic perspective: less energy is used when fewer neurons are firing.
94:. Information about the stimulus is encoded in this pattern of action potentials and transmitted into and around the brain. Beyond this, specialized neurons, such as those of the retina, can communicate more information through
255:— and this is the situation usually encountered in experimental protocols. Real-world input, however, is hardly stationary, but often changing on a fast time scale. For example, even when viewing a static image, humans perform
602:, or "spikes", within a spike train may carry additional information above and beyond the simple timing of the spikes. Early work suggested that correlation between spike trains can only reduce, and never increase, the total
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number of neurons in the population. This seems to be a hallmark of neural computations since compared to traditional computers, information is massively distributed across neurons. Sparse coding of natural images produces
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looking only at mean firing rates. Understanding any temporally encoded aspects of the neural code and replicating these sequences in neurons could allow for greater control and treatment of neurological disorders such as
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accumulating evidence for widespread sparse coding and theoretical arguments for its importance, a demonstration that sparse coding improves the stimulus-specificity of associative memory has been difficult to obtain.
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74:: voltage spikes that can travel down axons. Sensory neurons change their activities by firing sequences of action potentials in various temporal patterns, with the presence of external sensory stimuli, such as
533:. Within a cycle of gamma oscillation, each neuron has its own preferred relative firing time. As a result, an entire population of neurons generates a firing sequence that has a duration of up to about 15 ms.
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time-dependent firing rate, the experimenter records from a neuron while stimulating with some input sequence. The same stimulation sequence is repeated several times and the neuronal response is reported in a
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Han X, Qian X, Stern P, Chuong AS, Boyden ES. "Informational lesions: optical perturbations of spike timing and neural synchrony via microbial opsin gene fusions." Cambridge, Massachusetts: MIT Media Lad,
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is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. Sparseness is controlled by a negative feedback circuit between Kenyon cells and
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During rate coding, precisely calculating firing rate is very important. In fact, the term "firing rate" has a few different definitions, which refer to different averaging procedures, such as an
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Onken, A; Grünewälder, S; Munk, MHJ; Obermayer, K (2009), "Analyzing Short-Term Noise
Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation",
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Sengupta B, Laughlin SB, Niven JE (2014) Consequences of
Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency. PLOS Computational Biology 10(1): e1003439.
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different enough between similar (but not identical) stimuli to suggest that the distinct patterns of spikes contain a higher volume of information than is possible to include in a rate code.
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Maunsell JH, Van Essen DC (May 1983). "Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation".
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pattern of activity in the set of neurons. Vector coding is an example of simple averaging. A more sophisticated mathematical technique for performing such a reconstruction is the method of
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the phase are enough to represent all the information content in this kind of code with respect to the phase of oscillations in low frequencies. Phase-of-firing code is loosely based on the
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corresponding to the mean of the neuron with the greatest response. However, the noise inherent in neural responses means that a maximum likelihood estimation function is more accurate.
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based on a multivariate distribution of the neuronal responses. These models can assume independence, second order correlations, or even more detailed dependencies such as higher order
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Whether neurons use rate coding or temporal coding is a topic of intense debate within the neuroscience community, even though there is no clear definition of what these terms mean.
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that represent space, the precision of the population can scale exponentially with the number of neurons. This greatly reduces the number of neurons required for the same precision.
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Sachs, Murray B.; Young, Eric D. (November 1979). "Representation of steady-state vowels in the temporal aspects of the discharge patterns of populations of auditory-nerve fibers".
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practice, to get sensible averages, several spikes should occur within the time window. Typical values are T = 100 ms or T = 500 ms, but the duration may also be longer or shorter (
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274:. It has led to the idea that a neuron transforms information about a single input variable (the stimulus strength) into a single continuous output variable (the firing rate).
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allow neurologists to control spikes in individual neurons, offering electrical and spatial single-cell resolution. For example, blue light causes the light-gated ion channel
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refers to the reverse map, from response to stimulus, and the challenge is to reconstruct a stimulus, or certain aspects of that stimulus, from the spike sequences it evokes.
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Pati, Y. C.; Rezaiifar, R.; Krishnaprasad, P. S. (November 1993). "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition".
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for each input vector, so that a linear combination of the basis vectors with proportions given by the coefficients results in a close approximation to the input vector:
509:. This type of code takes into account a time label for each spike according to a time reference based on phase of local ongoing oscillations at low or high frequencies.
549:(MT), neurons are tuned to the direction of object motion. In response to an object moving in a particular direction, many neurons in MT fire with a noise-corrupted and
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of simple cells in the visual cortex. The capacity of sparse codes may be increased by simultaneous use of temporal coding, as found in the locust olfactory system.
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Neurons have an ability uncommon among the cells of the body to propagate signals rapidly over large distances by generating characteristic electrical pulses called
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is estimated to be overcomplete by a factor of 500, so that, for example, a 14 x 14 patch of input (a 196-dimensional space) is coded by roughly 100,000 neurons.
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average over N repeated runs. Thus, the time-dependent firing rate coding relies on the implicit assumption that there are always populations of neurons.
526:. Another feature of this code is that neurons adhere to a preferred order of spiking between a group of sensory neurons, resulting in firing sequence.
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also in the auditory and somato-sensory system. The main drawback of such a coding scheme is its sensitivity to intrinsic neuronal fluctuations. In the
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Schneidman, E; Berry, MJ; Segev, R; Bialek, W (2006), "Weak
Pairwise Correlations Imply Strongly Correlated Network States in a Neural Population",
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481:. Regulation of spike intervals in single cells more precisely controls brain activity than the addition of pharmacological agents intravenously.
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limit, as in high-contrast situations. For this reason, temporal coding may play a part in coding defined edges rather than gradual transitions.
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The specificity of temporal coding requires highly refined technology to measure informative, reliable, experimental data. Advances made in
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Olshausen, B. A.; Field, D. J. (1996). "Emergence of simple-cell receptive field properties by learning a sparse code for natural images".
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of an action potential (about 1 ms) is ignored, an action potential sequence, or spike train, can be characterized simply by a series of
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Karl
Diesseroth, Lecture. "Personal Growth Series: Karl Diesseroth on Cracking the Neural Code." Google Tech Talks. November 21, 2008.
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communicate via the time between spikes are also referred to as interpulse interval codes, and have been supported by recent studies.
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In the following decades, measurement of firing rates became a standard tool for describing the properties of all types of sensory or
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Butts DA, Weng C, Jin J, et al. (September 2007). "Temporal precision in the neural code and the timescales of natural vision".
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representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves.
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970:. These refer to the distribution of basis vector coefficients for typical inputs. A coding with soft sparseness has a smooth
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Despite its shortcomings, the concept of a spike-count rate code is widely used not only in experiments, but also in models of
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Brown EN, Kass RE, Mitra PP (May 2004). "Multiple neural spike train data analysis: state-of-the-art and future challenges".
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Wainrib, Gilles; Michèle, Thieullen; Khashayar, Pakdaman (7 April 2010). "Intrinsic variability of latency to first-spike".
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Miller, M.I.; Sachs, M.B. (1983). "Representation of stop consonants in the discharge patterns of auditory-nerve fibrers".
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than simply the average frequency of action potentials over a given period of time. This model is especially important for
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Sjöström, Jesper, and
Wulfram Gerstner. "Spike-timing dependent plasticity." Spike-timing dependent plasticity 35 (2010).
159:' is based on the precise timing of single spikes. They may be locked to an external stimulus such as in the visual and
3605:"A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields"
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Miller, M.I.; Sachs, M.B. (June 1984). "Representation of voice pitch in discharge patterns of auditory-nerve fibers".
1755:"Intracellular Calcium Dynamics Permit a Purkinje Neuron Model to Perform Toggle and Gain Computations Upon its Inputs"
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Merzenich, MM (Jun 1996). "Primary cortical representation of sounds by the coordination of action-potential timing".
998:. Overcomplete codings smoothly interpolate between input vectors and are robust under input noise. The human primary
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Most models of sparse coding are based on the linear generative model. In this model, the symbols are combined in a
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Needell, D.; Tropp, J.A. (2009-05-01). "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples".
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Vinje, WE; Gallant, JL (2000). "Sparse coding and decorrelation in primary visual cortex during natural vision".
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Wu S, Amari S, Nakahara H (May 2002). "Population coding and decoding in a neural field: a computational study".
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Gollisch, T.; Meister, M. (22 February 2008). "Rapid Neural Coding in the Retina with
Relative Spike Latencies".
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Zhang, Zhifeng; Mallat, Stephane G.; Davis, Geoffrey M. (July 1994). "Adaptive time-frequency decompositions".
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The codings generated by algorithms implementing a linear generative model can be classified into codings with
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Population coding has a number of other advantages as well, including reduction of uncertainty due to neuronal
382:, is that spikes occurring at specific phases of an oscillatory cycle are more effective in depolarizing the
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with time, the code is typically called a rate code, and if it varies rapidly, the code is called temporal.
2001:
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354:), employ those features of the spiking activity that cannot be described by the firing rate. For example,
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Montemurro, Marcelo A.; Rasch, Malte J.; Murayama, Yusuke; Logothetis, Nikos K.; Panzeri, Stefano (2008).
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J. Leo van Hemmen, TJ Sejnowski. 23 Problems in
Systems Neuroscience. Oxford Univ. Press, 2006. p.143-158.
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respond to any given stimulus and each neuron responds to only a few stimuli out of all possible stimuli.
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1471:"Mapping and deciphering neural codes of NMDA receptor-dependent fear memory engrams in the hippocampus"
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and shape, they are typically treated as identical stereotyped events in neural coding studies. If the
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Johnson, KO (Jun 1980). "Sensory discrimination: neural processes preceding discrimination decision".
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with respect to background oscillations, characteristics based on the second and higher statistical
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3477:"Emergence of simple-cell receptive field properties by learning a sparse code for natural images"
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Theunissen, F; Miller, JP (1995). "Temporal
Encoding in Nervous Systems: A Rigorous Definition".
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Stein RB, Gossen ER, Jones KE (May 2005). "Neuronal variability: noise or part of the signal?".
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Hallock, Robert M.; Di
Lorenzo, Patricia M. (2006). "Temporal coding in the gustatory system".
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for the stimuli to repeatedly present in an exactly same manner before generating a response.
1706:"The impulses produced by sensory nerve endings: Part II: The response of a single end organ"
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Until recently, scientists had put the most emphasis on rate encoding as an explanation for
4180:"On initial Brain Activity Mapping of episodic and semantic memory code in the hippocampus"
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3428:"Resolution of nested neuronal representations can be exponential in the number of neurons"
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selectivities, so that many neurons, but not necessarily all, respond to a given stimulus.
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Sparse, decorrelated odor coding in the mushroom body enhances learned odor discrimination
2746:"Synchrony makes neurons fire in sequence, and stimulus properties determine who is ahead"
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Kostal L, Lansky P, Rospars JP (November 2007). "Neuronal coding and spiking randomness".
8:
3654:
2228:
Jolivet, Renaud; Rauch, Alexander; Lüscher, Hans-Rudolf; Gerstner, Wulfram (2006-08-01).
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1963:
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1983:
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1754:
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1505:
1470:
1446:
1411:
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1196:
1136:
697:
603:
575:
412:
260:
211:
In rate coding, learning is based on activity-dependent synaptic weight modifications.
133:
formation. Neuroscientists have initiated several large-scale brain decoding projects.
122:
3693:
3676:
1232:
1215:
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2694:
2659:
2587:
2538:
2481:
2446:
2389:
2346:
2292:
2257:
2249:
2230:"Predicting spike timing of neocortical pyramidal neurons by simple threshold models"
2210:
2192:
2137:
2133:
2100:
2063:
2051:
1975:
1930:
1897:
1889:
1837:
1806:"The sodium-potassium pump is an information processing element in brain computation"
1786:
1735:
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1605:
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1451:
1384:
1372:
1328:
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1188:
555:
470:
310:
of trials on which a spike occurred between those times. Equivalently, r(t)Δt is the
71:
39:
35:
4094:
3796:
3161:
Amari, SL (2001), "Information Geometry on Hierarchy of Probability Distributions",
2493:
2477:
2149:
1013:
algorithm which finds the "best matching" projections of multidimensional data, and
4199:
4191:
4170:
4150:
4106:
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
4038:
4030:
3989:
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3938:
3899:
3849:
3829:
3774:
3733:
3688:
3619:
3568:
3560:
3519:
3499:
3452:
3447:
3427:
3387:
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
3372:
3352:
3307:
3299:
3260:
3224:
3214:
3180:
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2569:
2528:
2520:
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2436:
2428:
2401:
2381:
2358:
2338:
2269:
2241:
2200:
2184:
2129:
2043:
1987:
1967:
1926:
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
1909:
1881:
1827:
1817:
1776:
1766:
1725:
1721:
1717:
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1006:
624:
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461:
428:
383:
278:
186:
95:
3903:
3639:
1200:
351:
299:
264:
244:
189:, or "spike firing", increases. Rate coding is sometimes called frequency coding.
3994:
3977:
3943:
3219:
2726:
1924:
1678:
1541:
https://www.simonsfoundation.org/life-sciences/simons-collaboration-global-brain/
1495:
1436:
1322:
1277:
1141:
1131:
1096:
1063:
1035:
678:
271:
230:
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160:
143:
114:
110:
684:
Given a potentially large set of input patterns, sparse coding algorithms (e.g.
3833:
2808:
2690:
2573:
2524:
2432:
1306:
444:
378:(phase of firing). One way in which temporal codes are decoded, in presence of
259:, rapid changes of the direction of gaze. The image projected onto the retinal
181:
firing communication states that as the intensity of a stimulus increases, the
42:. Based on the theory that sensory and other information is represented in the
4195:
3778:
3623:
3564:
3264:
2851:
2654:
2637:
2608:
2385:
2245:
2002:"A consensus layer V pyramidal neuron can sustain interpulse-interval coding "
30:
field concerned with characterising the hypothetical relationship between the
4224:
3841:
3745:
2253:
2196:
1893:
1822:
1771:
1590:
1551:
Burcas G.T & Albright T.D. Gauging sensory representations in the brain.
1241:
1106:
1101:
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830:
474:
284:
156:
126:
59:
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4003:
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3911:
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3582:
3461:
3321:
3303:
3238:
3196:
3148:
3085:
2816:
2781:
2744:
Havenith MN, Yu S, Biederlack J, Chen NH, Singer W, Nikolić D (June 2011).
2698:
2663:
2638:"Phase-of-Firing Coding of Natural Visual Stimuli in Primary Visual Cortex"
2591:
2542:
2485:
2450:
2393:
2350:
2261:
2214:
2141:
1979:
1901:
1841:
1790:
1739:
1514:
1455:
1376:
1270:"Spike arrival times: A highly efficient coding scheme for neural networks"
1249:
1192:
457:
215:
55:
27:
4162:
3702:
3677:"Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1?"
3511:
3364:
3272:
3036:
2985:
2859:
2055:
1648:. Kistler, Werner M., 1969-. Cambridge, U.K.: Cambridge University Press.
1609:
3761:
Proceedings of 27th Asilomar Conference on Signals, Systems and Computers
2950:
2720:
Spike arrival times: A highly efficient coding scheme for neural networks
1643:
1273:
1086:
1059:
822:{\displaystyle {\vec {b_{1}}},\ldots ,{\vec {b_{n}}}\in \mathbb {R} ^{k}}
523:
440:
311:
3130:
2188:
1971:
703:
More formally, given a k-dimensional set of real-numbered input vectors
234:
on temporal averaging may be too simplistic to describe brain activity.
4065:
A sparse memory is a precise memory. Oxford Science blog. 28 Feb 2014.
3927:"Sparse representation of sounds in the unanesthetized auditory cortex"
3098:
2047:
1553:
http://www.vcl.salk.edu/Publications/PDF/Buracas_Albright_1999_TINS.pdf
1051:
952:{\displaystyle {\vec {\xi }}\approx \sum _{j=1}^{n}s_{j}{\vec {b}}_{j}}
3737:
3184:
3113:
647:
222:
in 1926. In this simple experiment different weights were hung from a
4154:
3503:
3356:
3028:
2942:
1067:
657:
182:
102:
87:
4034:
3288:"Correlations and the encoding of information in the nervous system"
1645:
Spiking neuron models : single neurons, populations, plasticity
1368:
1528:
1184:
256:
252:
4067:
http://www.ox.ac.uk/news/science-blog/sparse-memory-precise-memory
3824:
3653:
Lee, Honglak; Battle, Alexis; Raina, Rajat; Ng, Andrew Y. (2006).
3052:"Receptive fields of single neurones in the cat's striate cortex"
2635:
2163:
Gupta, Nitin; Singh, Swikriti Saran; Stopfer, Mark (2016-12-15).
1862:"Rapid Neural Coding in the Retina with Relative Spike Latencies"
674:
635:
501:
Phase-of-firing code is a neural coding scheme that combines the
1412:"Neural population-level memory traces in the mouse hippocampus"
616:
595:
223:
178:
51:
3978:"Synaptic mechanisms underlying sparse coding of active touch"
1324:
Spiking Neuron Models: Single Neurons, Populations, Plasticity
3549:"A temporal channel for information in sparse sensory coding"
2677:
Fries P, Nikolić D, Singer W (July 2007). "The gamma cycle".
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91:
83:
79:
75:
43:
2507:
Carleton, Alan; Accolla, Riccardo; Simon, Sidney A. (2010).
1564:
Gerstner W, Kreiter AK, Markram H, Herz AV (November 1997).
747:, the goal of sparse coding is to determine n k-dimensional
623:, or "spike", is independent of each other spike within the
3975:
3862:
Kanerva, Pentti. Sparse distributed memory. MIT press, 1988
2227:
829:, corresponding to neuronal receptive fields, along with a
529:
Phase code has been shown in visual cortex to involve also
291:
113:
point events in time. The lengths of interspike intervals (
34:
and the neuronal responses, and the relationship among the
4118:
Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W.
3976:
Crochet, S; Poulet, JFA; Kremer, Y; Petersen, CCH (2011).
3758:
3405:
Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W.
2558:"Neural and behavioral mechanisms of olfactory perception"
1563:
1399:
http://www.scientificamerican.com/article/the-memory-code/
285:
Time-dependent firing rate (averaging over several trials)
101:
Although action potentials can vary somewhat in duration,
3285:
2729:, SJ Thorpe - Parallel processing in neural systems, 1990
370:, spike randomness, or precisely timed groups of spikes (
2743:
1017:, a representation learning method which aims to find a
330:
When precise spike timing or high-frequency firing-rate
237:
163:
or be generated intrinsically by the neural circuitry.
16:
Method by which information is represented in the brain
2282:
883:
839:
756:
709:
405:
3924:
2506:
2029:
2027:
2025:
2023:
1676:
4019:"Sparse odor representation and olfactory learning"
2739:
2737:
2735:
2320:
2283:Geoffrois, E.; Edeline, J.M.; Vibert, J.F. (1994).
2119:
1469:Zhang, H; Chen, G; Kuang, H; Tsien, JZ (Nov 2013).
1468:
1279:
Parallel processing in neural systems and computers
4016:
3425:
2676:
1641:
951:
869:
821:
739:
263:changes therefore every few hundred milliseconds (
4122:. Cambridge, Massachusetts: The MIT Press; 1999.
4108:. Cambridge, Massachusetts: The MIT Press; 2001.
3662:Advances in Neural Information Processing Systems
3409:. Cambridge, Massachusetts: The MIT Press; 1999.
3389:. Cambridge, Massachusetts: The MIT Press; 2001.
2837:
2463:
2162:
2075:
2073:
2020:
740:{\displaystyle {\vec {\xi }}\in \mathbb {R} ^{k}}
4222:
3715:
3652:
3009:The Journal of the Acoustical Society of America
2923:The Journal of the Acoustical Society of America
2882:"Intro to Sensory Motor Systems Ch. 38 page 766"
2732:
2033:
1354:
833:n-dimensional vector of weights or coefficients
4017:Ito, I; Ong, RCY; Raman, B; Stopfer, M (2008).
2794:
2500:
2011:
1929:. Massachusetts Institute of Technology Press.
1859:
1703:
1677:Kandel, E.; Schwartz, J.; Jessel, T.M. (1991).
1317:
451:
314:that a spike occurs during this time interval.
4132:
3674:
3474:
2603:
2601:
2070:
1539:The Simons Collaboration on the Global Brain.
1170:
870:{\displaystyle {\vec {s}}\in \mathbb {R} ^{n}}
172:
149:
3675:Olshausen, Bruno A.; Field, David J. (1997).
2631:
2629:
2618:
2616:
1409:
4081:." Nature Neuroscience 17.4 (2014): 559-568.
3925:Hromádka, T; Deweese, MR; Zador, AM (2008).
3871:
3809:
3546:
3426:Mathis A, Herz AV, Stemmler MB (July 2012).
2165:"Oscillatory integration windows in neurons"
2105:: CS1 maint: multiple names: authors list (
1949:
1307:https://doi.org/10.1371/journal.pcbi.1003439
277:There is a growing body of evidence that in
204:(rate as a single-neuron spike count) or an
3812:Applied and Computational Harmonic Analysis
3603:Rehn, Martin; Sommer, Friedrich T. (2007).
3475:Olshausen, Bruno A; Field, David J (1996).
3049:
3006:
2963:
2670:
2609:https://www.youtube.com/watch?v=5SLdSbp6VjM
2598:
1922:
986:Another measure of coding is whether it is
610:
247:in the textbook 'Spiking Neuron Models' ).
3602:
2920:
2626:
2613:
2509:"Coding in the mammalian gustatory system"
2079:
1803:
1752:
1557:
691:
651:Neural responses are noisy and unreliable.
505:count code with a time reference based on
4203:
4042:
3993:
3952:
3942:
3893:
3823:
3768:
3692:
3668:
3572:
3451:
3334:
3311:
3228:
3218:
3174:
3160:
3138:
3112:
3075:
2771:
2761:
2653:
2581:
2532:
2440:
2289:Computation in Neurons and Neural Systems
2204:
2156:
1831:
1821:
1780:
1770:
1729:
1599:
1589:
1504:
1494:
1445:
1435:
1231:
857:
809:
727:
677:-like oriented filters that resemble the
522:phenomena observed in place cells of the
3286:Panzeri; Schultz; Treves; Rolls (1999).
2831:
2466:Neuroscience & Biobehavioral Reviews
1860:Gollisch, T.; Meister, M. (2008-02-22).
1263:
1261:
1259:
646:
634:
598:firing claims that correlations between
136:
3598:
3596:
3594:
3592:
3547:Gupta, N; Stopfer, M (6 October 2014).
3250:
3163:IEEE Transactions on Information Theory
1759:Frontiers in Computational Neuroscience
1566:"Neural codes: firing rates and beyond"
1350:
1348:
1346:
1344:
1311:
1213:
484:
4223:
2555:
2414:
2113:
1943:
1670:
1267:
1024:
615:The independent-spike coding model of
4177:
3612:Journal of Computational Neuroscience
3043:
2911:Science. 1986 Sep 26;233(4771):1416-9
2234:Journal of Computational Neuroscience
2036:Journal of Computational Neuroscience
1916:
1855:
1853:
1851:
1637:
1635:
1633:
1631:
1629:
1627:
1625:
1623:
1621:
1619:
1410:Chen, G; Wang, LP; Tsien, JZ (2009).
1256:
1034:in which only a few neurons out of a
589:
3655:"Efficient sparse coding algorithms"
3589:
3050:Hubel DH, Wiesel TN (October 1959).
1923:Dayan, Peter; Abbott, L. F. (2001).
1341:
1164:
536:
238:Spike-count rate (average over time)
214:Rate coding was originally shown by
4184:Neurobiology of Learning and Memory
3646:
3419:
2086:© Current Biology 1995, Vol 5 No 12
619:firing claims that each individual
13:
4087:
2788:
2080:Zador, Stevens, Charles, Anthony.
1848:
1616:
1272:. In Eckmiller, R.; Hartmann, G.;
630:
406:Temporal coding in sensory systems
325:
14:
4252:
4120:Spikes: Exploring the Neural Code
3407:Spikes: Exploring the Neural Code
2285:"Learning by Delay Modifications"
1285:. North-Holland. pp. 91–94.
396:spike-timing-dependent plasticity
4178:Tsien, JZ.; et al. (2014).
2134:10.1111/j.1460-9568.2007.05880.x
1529:http://braindecodingproject.org/
663:
594:The correlation coding model of
545:For example, in the visual area
206:average over several repetitions
4071:
4059:
4010:
3969:
3918:
3865:
3856:
3803:
3752:
3709:
3540:
3468:
3399:
3379:
3328:
3279:
3244:
3190:
3154:
3092:
3000:
2957:
2914:
2905:
2874:
2713:
2562:Current Opinion in Neurobiology
2549:
2478:10.1016/j.neubiorev.2006.07.005
2457:
2421:Current Opinion in Neurobiology
2408:
2365:
2314:
2305:
2276:
2221:
1994:
1797:
1746:
1704:Adrian ED, Zotterman Y (1926).
1697:
1545:
1533:
1521:
639:Plot of typical position coding
3453:10.1103/PhysRevLett.109.018103
3068:10.1113/jphysiol.1959.sp006308
2763:10.1523/JNEUROSCI.2817-10.2011
2287:. In Eeckman, Frank H. (ed.).
1722:10.1113/jphysiol.1926.sp002281
1462:
1403:
1391:
1327:. Cambridge University Press.
1299:
1207:
937:
890:
846:
798:
770:
716:
439:As with the visual system, in
208:(rate of PSTH) of experiment.
1:
3904:10.1126/science.287.5456.1273
3694:10.1016/s0042-6989(97)00169-7
1321:; Kistler, Werner M. (2002).
1233:10.1016/S0896-6273(00)81193-9
1158:
3995:10.1016/j.neuron.2011.02.022
3944:10.1371/journal.pbio.0060016
3220:10.1371/journal.pcbi.1000577
2978:10.1016/0378-5955(84)90054-6
2415:Victor, Johnathan D (2005).
2291:. Springer. pp. 133–8.
1804:Forrest MD (December 2014).
1680:Principles of Neural Science
1570:Proc. Natl. Acad. Sci. U.S.A
1496:10.1371/journal.pone.0079454
1437:10.1371/journal.pone.0008256
1214:Johnson, K. O. (June 2000).
1122:Models of neural computation
1058:, sparse odor coding by the
452:Temporal coding applications
350:Temporal codes (also called
292:Peri-Stimulus-Time Histogram
7:
1642:Gerstner, Wulfram. (2002).
1074:
531:high-frequency oscillations
173:Traditional View: Rate Code
150:Hypothesized coding schemes
65:
10:
4257:
4236:Computational neuroscience
3834:10.1016/j.acha.2008.07.002
2809:10.1162/089976602753633367
2691:10.1016/j.tins.2007.05.005
2574:10.1016/j.conb.2008.08.015
2525:10.1016/j.tins.2010.04.002
2433:10.1016/j.conb.2005.08.002
1683:(3rd ed.). Elsevier.
1112:Feature integration theory
1005:Other models are based on
700:to approximate the input.
497:Phase resetting in neurons
494:
488:
358:after the stimulus onset,
129:have been widely applied.
4196:10.1016/j.nlm.2013.06.019
4104:Dayan P & Abbott LF.
3779:10.1109/ACSSC.1993.342465
3624:10.1007/s10827-006-0003-9
3565:10.1016/j.cub.2014.08.021
3385:Dayan P & Abbott LF.
3265:10.1152/jn.1980.43.6.1793
2852:10.1152/jn.1983.49.5.1127
2655:10.1016/j.cub.2008.02.023
2556:Wilson, Rachel I (2008).
2386:10.1007/s00422-010-0384-8
2246:10.1007/s10827-006-7074-5
2082:"The enigma of the brain"
1147:Sparse distributed memory
1082:Artificial neural network
1043:sparse distributed memory
376:ongoing brain oscillation
177:The rate coding model of
4077:Lin, Andrew C., et al. "
3763:. pp. 40–44 vol.1.
1823:10.3389/fphys.2014.00472
1772:10.3389/fncom.2014.00086
1591:10.1073/pnas.94.24.12740
1527:Brain Decoding Project.
611:Independent-spike coding
368:probability distribution
2513:Trends in Neurosciences
2343:10.1126/science.1149639
1886:10.1126/science.1149639
1810:Frontiers in Physiology
1092:Biological neuron model
692:Linear generative model
344:post-synaptic potential
3304:10.1098/rspb.1999.0736
2374:Biological Cybernetics
953:
919:
871:
823:
741:
652:
640:
580:maximum entropy models
50:, it is believed that
38:of the neurons in the
4093:Földiák P, Endres D,
2417:"Spike train metrics"
2169:Nature Communications
1268:Thorpe, S.J. (1990).
954:
899:
872:
824:
742:
650:
638:
515:local field potential
495:Further information:
421:primary visual cortex
137:Encoding and decoding
36:electrical activities
24:neural representation
1041:Theoretical work on
1032:associative memories
1011:sparse approximation
881:
837:
754:
707:
669:locations is known.
485:Phase-of-firing code
384:post-synaptic neuron
4147:1996Natur.381..607O
3886:2000Sci...287.1273V
3880:(5456): 1273–1276.
3730:1994OptEn..33.2183D
3718:Optical Engineering
3496:1996Natur.381..607O
3444:2012PhRvL.109a8103M
3349:1996Natur.381..610D
3211:2009PLSCB...5E0577O
3131:10.1038/nature04701
3123:2006Natur.440.1007S
3107:(7087): 1007–1012,
3021:1983ASAJ...74..502M
2935:1979ASAJ...66.1381Y
2335:2008Sci...319.1108G
2329:(5866): 1108–1111.
2189:10.1038/ncomms13808
2181:2016NatCo...713808G
1972:10.1038/nature06105
1964:2007Natur.449...92B
1878:2008Sci...319.1108G
1872:(5866): 1108–1111.
1753:Forrest MD (2014).
1582:1997PNAS...9412740G
1487:2013PLoSO...879454Z
1428:2009PLoSO...4.8256C
1152:Vector quantization
1025:Biological evidence
1015:dictionary learning
988:critically complete
479:Parkinson's disease
441:mitral/tufted cells
380:neural oscillations
356:time-to-first-spike
119:statistical methods
48:networks of neurons
4101:, 3(1):2984, 2008.
2725:2012-02-15 at the
2048:10.1007/bf00961885
2000:Singh & Levy,
1357:Nat. Rev. Neurosci
1137:Neural oscillation
1030:stimulus-specific
949:
867:
819:
737:
686:sparse autoencoder
653:
641:
604:mutual information
590:Correlation coding
576:maximum likelihood
413:sound localization
123:probability theory
4029:(10): 1177–1184.
3788:978-0-8186-4120-6
3738:10.1117/12.173207
3687:(23): 3311–3325.
3490:(6583): 607–609.
3298:(1423): 1001–12.
3185:10.1109/18.930911
2298:978-0-7923-9465-5
1936:978-0-262-04199-7
1397:The Memory Code.
1334:978-0-521-89079-3
1319:Gerstner, Wulfram
1292:978-0-444-88390-2
940:
893:
849:
801:
773:
719:
600:action potentials
556:population vector
537:Population coding
372:temporal patterns
202:average over time
187:action potentials
96:graded potentials
72:action potentials
4248:
4241:Neural circuitry
4217:
4207:
4174:
4155:10.1038/381607a0
4082:
4075:
4069:
4063:
4057:
4056:
4046:
4014:
4008:
4007:
3997:
3988:(6): 1160–1175.
3973:
3967:
3966:
3956:
3946:
3922:
3916:
3915:
3897:
3869:
3863:
3860:
3854:
3853:
3827:
3807:
3801:
3800:
3772:
3756:
3750:
3749:
3724:(7): 2183–2192.
3713:
3707:
3706:
3696:
3672:
3666:
3665:
3659:
3650:
3644:
3643:
3609:
3600:
3587:
3586:
3576:
3544:
3538:
3537:
3535:
3534:
3528:
3522:. Archived from
3504:10.1038/381607a0
3481:
3472:
3466:
3465:
3455:
3423:
3417:
3403:
3397:
3383:
3377:
3376:
3357:10.1038/381610a0
3332:
3326:
3325:
3315:
3283:
3277:
3276:
3248:
3242:
3241:
3232:
3222:
3205:(11): e1000577,
3199:PLOS Comput Biol
3194:
3188:
3187:
3178:
3169:(5): 1701–1711,
3158:
3152:
3151:
3142:
3116:
3096:
3090:
3089:
3079:
3047:
3041:
3040:
3029:10.1121/1.389816
3004:
2998:
2997:
2966:Hearing Research
2961:
2955:
2954:
2943:10.1121/1.383532
2929:(5): 1381–1403.
2918:
2912:
2909:
2903:
2902:
2900:
2899:
2893:
2887:. Archived from
2886:
2878:
2872:
2871:
2835:
2829:
2828:
2792:
2786:
2785:
2775:
2765:
2741:
2730:
2717:
2711:
2710:
2674:
2668:
2667:
2657:
2633:
2624:
2620:
2611:
2605:
2596:
2595:
2585:
2553:
2547:
2546:
2536:
2504:
2498:
2497:
2472:(8): 1145–1160.
2461:
2455:
2454:
2444:
2412:
2406:
2405:
2369:
2363:
2362:
2318:
2312:
2309:
2303:
2302:
2280:
2274:
2273:
2225:
2219:
2218:
2208:
2160:
2154:
2153:
2128:(10): 2693–701.
2122:Eur. J. Neurosci
2117:
2111:
2110:
2104:
2096:
2094:
2092:
2077:
2068:
2067:
2031:
2018:
2015:
2009:
1998:
1992:
1991:
1947:
1941:
1940:
1920:
1914:
1913:
1857:
1846:
1845:
1835:
1825:
1801:
1795:
1794:
1784:
1774:
1750:
1744:
1743:
1733:
1701:
1695:
1694:
1674:
1668:
1667:
1639:
1614:
1613:
1603:
1593:
1561:
1555:
1549:
1543:
1537:
1531:
1525:
1519:
1518:
1508:
1498:
1466:
1460:
1459:
1449:
1439:
1407:
1401:
1395:
1389:
1388:
1352:
1339:
1338:
1315:
1309:
1303:
1297:
1296:
1284:
1265:
1254:
1253:
1235:
1211:
1205:
1204:
1168:
1127:Neural correlate
1117:Grandmother cell
1056:olfactory system
1007:matching pursuit
958:
956:
955:
950:
948:
947:
942:
941:
933:
929:
928:
918:
913:
895:
894:
886:
876:
874:
873:
868:
866:
865:
860:
851:
850:
842:
828:
826:
825:
820:
818:
817:
812:
803:
802:
797:
796:
787:
775:
774:
769:
768:
759:
746:
744:
743:
738:
736:
735:
730:
721:
720:
712:
679:receptive fields
621:action potential
520:phase precession
491:Phase precession
462:channelrhodopsin
429:gustatory system
279:Purkinje neurons
251:reaction of the
54:can encode both
4256:
4255:
4251:
4250:
4249:
4247:
4246:
4245:
4221:
4220:
4141:(6583): 607–9.
4090:
4088:Further reading
4085:
4076:
4072:
4064:
4060:
4035:10.1038/nn.2192
4015:
4011:
3974:
3970:
3923:
3919:
3895:10.1.1.456.2467
3870:
3866:
3861:
3857:
3808:
3804:
3789:
3770:10.1.1.348.5735
3757:
3753:
3714:
3710:
3681:Vision Research
3673:
3669:
3657:
3651:
3647:
3607:
3601:
3590:
3559:(19): 2247–56.
3553:Current Biology
3545:
3541:
3532:
3530:
3526:
3479:
3473:
3469:
3432:Phys. Rev. Lett
3424:
3420:
3404:
3400:
3384:
3380:
3343:(6583): 610–3.
3333:
3329:
3284:
3280:
3259:(6): 1793–815.
3249:
3245:
3195:
3191:
3159:
3155:
3097:
3093:
3048:
3044:
3005:
3001:
2962:
2958:
2919:
2915:
2910:
2906:
2897:
2895:
2891:
2884:
2880:
2879:
2875:
2840:J. Neurophysiol
2836:
2832:
2803:(5): 999–1026.
2793:
2789:
2756:(23): 8570–84.
2742:
2733:
2727:Wayback Machine
2718:
2714:
2679:Trends Neurosci
2675:
2671:
2642:Current Biology
2634:
2627:
2621:
2614:
2606:
2599:
2554:
2550:
2505:
2501:
2462:
2458:
2413:
2409:
2370:
2366:
2319:
2315:
2310:
2306:
2299:
2281:
2277:
2226:
2222:
2161:
2157:
2118:
2114:
2098:
2097:
2090:
2088:
2078:
2071:
2032:
2021:
2016:
2012:
1999:
1995:
1948:
1944:
1937:
1921:
1917:
1858:
1849:
1802:
1798:
1751:
1747:
1702:
1698:
1691:
1675:
1671:
1656:
1640:
1617:
1576:(24): 12740–1.
1562:
1558:
1550:
1546:
1538:
1534:
1526:
1522:
1467:
1463:
1408:
1404:
1396:
1392:
1369:10.1038/nrn1668
1353:
1342:
1335:
1316:
1312:
1304:
1300:
1293:
1282:
1266:
1257:
1216:"Neural coding"
1212:
1208:
1169:
1165:
1161:
1156:
1142:Receptive field
1132:Neural decoding
1097:Binding problem
1077:
1027:
968:hard sparseness
966:and those with
964:soft sparseness
943:
932:
931:
930:
924:
920:
914:
903:
885:
884:
882:
879:
878:
861:
856:
855:
841:
840:
838:
835:
834:
813:
808:
807:
792:
788:
786:
785:
764:
760:
758:
757:
755:
752:
751:
731:
726:
725:
711:
710:
708:
705:
704:
694:
666:
633:
631:Position coding
613:
592:
547:medial temporal
539:
499:
493:
487:
454:
408:
360:phase-of-firing
328:
326:Temporal coding
297:
287:
272:neural networks
240:
220:Yngve Zotterman
175:
169:
161:auditory system
152:
144:Neural decoding
139:
127:point processes
125:and stochastic
121:and methods of
68:
17:
12:
11:
5:
4254:
4244:
4243:
4238:
4233:
4219:
4218:
4175:
4130:
4116:
4102:
4089:
4086:
4084:
4083:
4070:
4058:
4009:
3968:
3917:
3864:
3855:
3818:(3): 301–321.
3802:
3787:
3751:
3708:
3667:
3645:
3618:(2): 135–146.
3588:
3539:
3467:
3418:
3398:
3378:
3327:
3278:
3253:J Neurophysiol
3243:
3189:
3176:10.1.1.46.5226
3153:
3091:
3042:
3015:(2): 502–517.
2999:
2972:(3): 257–279.
2956:
2913:
2904:
2873:
2846:(5): 1127–47.
2830:
2787:
2731:
2712:
2669:
2648:(5): 375–380.
2625:
2612:
2597:
2568:(4): 408–412.
2548:
2519:(7): 326–334.
2499:
2456:
2427:(5): 585–592.
2407:
2364:
2313:
2304:
2297:
2275:
2220:
2155:
2112:
2069:
2042:(2): 149–162.
2019:
2010:
1993:
1958:(7158): 92–5.
1942:
1935:
1915:
1847:
1796:
1745:
1716:(2): 151–171.
1696:
1690:978-0444015624
1689:
1669:
1654:
1615:
1556:
1544:
1532:
1520:
1481:(11): e79454.
1461:
1402:
1390:
1340:
1333:
1310:
1298:
1291:
1255:
1226:(3): 563–566.
1206:
1185:10.1038/nn1228
1162:
1160:
1157:
1155:
1154:
1149:
1144:
1139:
1134:
1129:
1124:
1119:
1114:
1109:
1104:
1099:
1094:
1089:
1084:
1078:
1076:
1073:
1026:
1023:
946:
939:
936:
927:
923:
917:
912:
909:
906:
902:
898:
892:
889:
864:
859:
854:
848:
845:
816:
811:
806:
800:
795:
791:
784:
781:
778:
772:
767:
763:
734:
729:
724:
718:
715:
698:linear fashion
693:
690:
665:
662:
632:
629:
612:
609:
591:
588:
538:
535:
489:Main article:
486:
483:
453:
450:
445:olfactory bulb
427:The mammalian
407:
404:
327:
324:
295:
286:
283:
261:photoreceptors
239:
236:
174:
171:
151:
148:
138:
135:
107:brief duration
67:
64:
15:
9:
6:
4:
3:
2:
4253:
4242:
4239:
4237:
4234:
4232:
4231:Neural coding
4229:
4228:
4226:
4215:
4211:
4206:
4201:
4197:
4193:
4189:
4185:
4181:
4176:
4172:
4168:
4164:
4160:
4156:
4152:
4148:
4144:
4140:
4136:
4131:
4129:
4128:0-262-68108-0
4125:
4121:
4117:
4115:
4114:0-262-04199-5
4111:
4107:
4103:
4100:
4096:
4095:Sparse coding
4092:
4091:
4080:
4074:
4068:
4062:
4054:
4050:
4045:
4040:
4036:
4032:
4028:
4024:
4020:
4013:
4005:
4001:
3996:
3991:
3987:
3983:
3979:
3972:
3964:
3960:
3955:
3950:
3945:
3940:
3936:
3932:
3928:
3921:
3913:
3909:
3905:
3901:
3896:
3891:
3887:
3883:
3879:
3875:
3868:
3859:
3851:
3847:
3843:
3839:
3835:
3831:
3826:
3821:
3817:
3813:
3806:
3798:
3794:
3790:
3784:
3780:
3776:
3771:
3766:
3762:
3755:
3747:
3743:
3739:
3735:
3731:
3727:
3723:
3719:
3712:
3704:
3700:
3695:
3690:
3686:
3682:
3678:
3671:
3663:
3656:
3649:
3641:
3637:
3633:
3629:
3625:
3621:
3617:
3613:
3606:
3599:
3597:
3595:
3593:
3584:
3580:
3575:
3570:
3566:
3562:
3558:
3554:
3550:
3543:
3529:on 2015-11-23
3525:
3521:
3517:
3513:
3509:
3505:
3501:
3497:
3493:
3489:
3485:
3478:
3471:
3463:
3459:
3454:
3449:
3445:
3441:
3438:(1): 018103.
3437:
3433:
3429:
3422:
3416:
3415:0-262-68108-0
3412:
3408:
3402:
3396:
3395:0-262-04199-5
3392:
3388:
3382:
3374:
3370:
3366:
3362:
3358:
3354:
3350:
3346:
3342:
3338:
3331:
3323:
3319:
3314:
3309:
3305:
3301:
3297:
3293:
3292:Proc Biol Sci
3289:
3282:
3274:
3270:
3266:
3262:
3258:
3254:
3247:
3240:
3236:
3231:
3226:
3221:
3216:
3212:
3208:
3204:
3200:
3193:
3186:
3182:
3177:
3172:
3168:
3164:
3157:
3150:
3146:
3141:
3136:
3132:
3128:
3124:
3120:
3115:
3114:q-bio/0512013
3110:
3106:
3102:
3095:
3087:
3083:
3078:
3073:
3069:
3065:
3062:(3): 574–91.
3061:
3057:
3053:
3046:
3038:
3034:
3030:
3026:
3022:
3018:
3014:
3010:
3003:
2995:
2991:
2987:
2983:
2979:
2975:
2971:
2967:
2960:
2952:
2948:
2944:
2940:
2936:
2932:
2928:
2924:
2917:
2908:
2894:on 2012-05-11
2890:
2883:
2877:
2869:
2865:
2861:
2857:
2853:
2849:
2845:
2841:
2834:
2826:
2822:
2818:
2814:
2810:
2806:
2802:
2798:
2797:Neural Comput
2791:
2783:
2779:
2774:
2769:
2764:
2759:
2755:
2751:
2747:
2740:
2738:
2736:
2728:
2724:
2721:
2716:
2708:
2704:
2700:
2696:
2692:
2688:
2685:(7): 309–16.
2684:
2680:
2673:
2665:
2661:
2656:
2651:
2647:
2643:
2639:
2632:
2630:
2619:
2617:
2610:
2604:
2602:
2593:
2589:
2584:
2579:
2575:
2571:
2567:
2563:
2559:
2552:
2544:
2540:
2535:
2530:
2526:
2522:
2518:
2514:
2510:
2503:
2495:
2491:
2487:
2483:
2479:
2475:
2471:
2467:
2460:
2452:
2448:
2443:
2438:
2434:
2430:
2426:
2422:
2418:
2411:
2403:
2399:
2395:
2391:
2387:
2383:
2379:
2375:
2368:
2360:
2356:
2352:
2348:
2344:
2340:
2336:
2332:
2328:
2324:
2317:
2308:
2300:
2294:
2290:
2286:
2279:
2271:
2267:
2263:
2259:
2255:
2251:
2247:
2243:
2239:
2235:
2231:
2224:
2216:
2212:
2207:
2202:
2198:
2194:
2190:
2186:
2182:
2178:
2174:
2170:
2166:
2159:
2151:
2147:
2143:
2139:
2135:
2131:
2127:
2123:
2116:
2108:
2102:
2087:
2083:
2076:
2074:
2065:
2061:
2057:
2053:
2049:
2045:
2041:
2037:
2030:
2028:
2026:
2024:
2014:
2007:
2003:
1997:
1989:
1985:
1981:
1977:
1973:
1969:
1965:
1961:
1957:
1953:
1946:
1938:
1932:
1928:
1927:
1919:
1911:
1907:
1903:
1899:
1895:
1891:
1887:
1883:
1879:
1875:
1871:
1867:
1863:
1856:
1854:
1852:
1843:
1839:
1834:
1829:
1824:
1819:
1815:
1811:
1807:
1800:
1792:
1788:
1783:
1778:
1773:
1768:
1764:
1760:
1756:
1749:
1741:
1737:
1732:
1727:
1723:
1719:
1715:
1711:
1707:
1700:
1692:
1686:
1682:
1681:
1673:
1665:
1661:
1657:
1655:0-511-07817-X
1651:
1647:
1646:
1638:
1636:
1634:
1632:
1630:
1628:
1626:
1624:
1622:
1620:
1611:
1607:
1602:
1597:
1592:
1587:
1583:
1579:
1575:
1571:
1567:
1560:
1554:
1548:
1542:
1536:
1530:
1524:
1516:
1512:
1507:
1502:
1497:
1492:
1488:
1484:
1480:
1476:
1472:
1465:
1457:
1453:
1448:
1443:
1438:
1433:
1429:
1425:
1422:(12): e8256.
1421:
1417:
1413:
1406:
1400:
1394:
1386:
1382:
1378:
1374:
1370:
1366:
1363:(5): 389–97.
1362:
1358:
1351:
1349:
1347:
1345:
1336:
1330:
1326:
1325:
1320:
1314:
1308:
1302:
1294:
1288:
1281:
1280:
1275:
1271:
1264:
1262:
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